Last Updated：2025/12/08
Sentence
glₙ の多項式表現の不変量を研究する際に、カペッリの恒等式は、非可換元を持つ行列に対する det(AB) = det(A) det(B) の類似であり、ケイリーの Ω 演算を通して不変量 f を Ωf に結びつけます。
Quizzes for review
When studying the invariants of polynomial representations of glₙ, Capelli's identity provides a noncommutative analogue of det(AB) = det(A) det(B) that relates an invariant f to Ωf via Cayley's Ω process.
See correct answer
When studying the invariants of polynomial representations of glₙ, Capelli's identity provides a noncommutative analogue of det(AB) = det(A) det(B) that relates an invariant f to Ωf via Cayley's Ω process.
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Related words
Capelli's identity
Proper noun
Japanese Meaning
数学における公式で、非可換な項目を持つ特定の行列に対して、det(AB)=det(A)det(B)の関係の類推として成立する。特に、Lie代数glₙの表現論に関連し、CayleyのΩ過程（Ω）を介して、不変量ƒとその変形Ωƒとの関係を結びつけるために用いられる。
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